The present invention relates to an anti-rolling structure for a box-type floating body such as a hull of a work-ship or -vessel or a hull for FPSO (Floating Production, Storage and Off-Loading).
In recent years, various new types of active anti-rolling systems for reducing roll motion of a hull in waves have been studied and some of them are already in practical use. Active anti-rolling systems are evidently superior to passive ones in terms of their roll reducing effect.
However, various active anti-rolling systems for reducing roll motion of hulls are generally complicated in structure, large-sized and heavy-weighted and require a large installation space. For reasons of economy and space, such systems are usually difficult to adopt for hulls.
Then, studies have been consequently made on passive anti-rolling systems which reduce roll motion by devising specifications and forms of hulls. A result of such studies was published in the bulletin of the Kansai Society of Naval Architects, extra volume with issue number 232 (September 1999). xe2x80x9cSeveral studies on reducing roll motion in wavesxe2x80x9d (pp 63-70) is a paper of studies published in this bulletin. According to the paper, roll motion of box-type floating bodies can be reduced by adjusting height of the center of gravity. The content of the paper is now referred to below.
FIG. 1 shows an example of a box-type floating body 1 seen from the rear. The floating body 1 has a breadth B and a draft d. A center G of gravity of the floating body 1 is located near an origin O at which a waterline lies, or for example, a little above the origin O.
When the box-type floating body 1 as described above is subjected to beam seas, rolling motion 2 is generated which acts to rotate the floating body 1 around the center G of gravity.
The paper studies on reduction of roll motion of the box-type floating body 1 having a large ratio of the breadth B to the draft d (a large breadth/draft ratio) and argues that the roll motion can be reduced by shifting the position of the center G of gravity of the floating body 1.
Theoretical foundation of the study is an equation of motion with one degree of freedom for roll motion (rolling) having a synchronous influence on sway motion (swaying). Here the sway motion means a motion in which the box-type floating body 1 horizontally moves to right and left; and the roll motion, a motion in which the floating body 1 rotationally moves around the center G of gravity. An equation of motion with one degree of freedom, which is expressed in a more simple form, is useful in estimating a possibility of the reduction of roll motion.
An equation of motion with one degree of freedom for roll motion in which simultaneousness of the sway and rolling motions is considered is given as follows from an equation of synchronized motion of rolling and swaying:                                           [                                          D                4                            -                                                D                  24                  2                                                  D                  2                                                      ]                    ⁢                                    X              4                                      ζ              A                                      =                              H            4                    -                                                    D                24                                            D                2                                      ⁢                          H              2                                                          (        1        )            
where X4 is an amplitude of the roll motion; Hj (j=2, 4), the Kochin function; Dj and D24, coefficients that depend on hydrodynamic force; and j=2 and 4, the sway motion and the roll motion, respectively.
The right-hand side of Equation (1) is the wave exciting moment of roll motion in a broad sense, which includes influence from the sway motion. A relationship is formed as the equation below between the wave exciting moment of roll motion and effective wave slope coefficient xcex3.                               γ          ·          GM                =                              -            i                    ⁢                      xe2x80x83                    ⁢                                                    H                4                            -                                                (                                                            D                      24                                        /                                          D                      2                                                        )                                ⁢                                  H                  2                                                                    K              ⁢                              xe2x80x83                            ⁢                              ∇                                  /                                      (                                          B                      /                      2                                        )                                                                                                          (        2        )            
Next, define an added mass coefficient k2 of sway motion, hydrodynamic force lever l2 and wave exciting moment lever lw, giving                                                                                           k                  2                                =                                                                            m                      22                                        /                    ρ                                    ⁢                                      xe2x80x83                                    ∇                                                                                                                          l                  2                                =                                                      -                                          m                      24                                                        /                                      m                    22                                                                                                                                                                l                    w                                    /                                      (                                          B                      /                      2                                        )                                                  =                                                      -                                          H                      4                                                        /                                      H                    2                                                                                      }                            (        3        )            
where l2 and lw are distances measured from the center G of gravity of the box-type floating body 1 to the points where respective forces act and are defined as positive toward upwards.
With l20 and lwo as moment levers being defined about the origin O, giving
l(K)=k2l20xe2x88x92(1+k2)lwoxe2x80x83xe2x80x83(4)
When
xcex3s=(i/K∇){H2/(1+k2)}xe2x80x83xe2x80x83(5)
holds, Equation (2) can be rewritten as
xcex3xc2x7GM=xcex3s{OGxe2x88x921(K)}xe2x80x83xe2x80x83(6),
where OG is distance from the origin O lying at the waterline to the center G of gravity and is defined as positive when the center G of gravity is located below the origin O; GM is height of the metacenter M (the distance from the center G of gravity to the metacenter M).
xcex3s corresponds to an approximate value of the amplitude of single sway motion, and a moment lever l(K) is a value independent of the location of the center of gravity. Both xcex3s and l(K) depend on the shape and motion frequency of the box-type floating body 1.
xcex3s, a component of an effective wave slope coefficient, and the moment lever l(K) were calculated on the box-type floating body 1. The floating body l on which the calculations are made has six different values of B/d: 2.5, 5, 7.5, 10, 12.5 and 20. The two-dimensional velocity potential continuation method is used for calculation in which three-dimensional influence on a hydrodynamic force is not considered.
Calculated values of xcex3s are shown in FIG. 2. The abscissa in FIG. 2 represents a non-dimensional frequency K(B/2) where K=xcfx892/g, xcfx89=2xcfx80/T, and xcfx89 and T are a frequency and wave period, respectively.
As shown in FIG. 2, xcex3s flatly decreases as the frequency increases. xcex3s changes a little with a change in the breadth/draft ratio of the box-type floating body 1; in shallow-draft box-type floating bodies having a B/d ratio of 5 or more, the values of xcex3s may be regarded as similar.
FIG. 3 shows the relationship between the ratio of the moment lever l(K) to a half-breadth B/2, or l(K)/(B/2) (the ordinate), and the non-dimensional frequency K(B/2) (the abscissa) with B/d as a parameter. l(K)/(B/2) varies slightly against the frequency, but varies considerably with the breadth/draft ratio. The greater the B/d, the greater the absolute value of l(K)/(B/2). With B/d=5, l(K)/(B/d) is nearly zero, showing substantially no change against the frequency. The value of 1(K) is obtainable from FIG. 3 if both the breadth/draft ratio B/d and the wave frequency of a sea area where the floating structure is installed are given.
There are three fundamental ideas to reduce the motion of a box-type floating body in waves: increase in damping force, prolongation of the natural period of the motion and reduction in the wave exciting force. In the equation (1) of synchronized motion, reducing the wave exciting force means to make smaller the value of the right-hand side, which can be achieved by making xcex3xc2x7GM smaller as can be seen from Equation (2). Since xcex3xc2x7GM can be expressed as Equation (6), xcex3xc2x7GM=0 either when xcex3s=0 at a certain frequency or when OG=l(K). In this paper reduction in roll motion is realized with this idea.
First, H2(K)=0 is needed in order to have xcex3s=0, which is theoretically achievable by selecting the shape of a floating body which has no sway waves. However, realistic shapes may not be obtainable for box-type floating bodies having larger breadth/draft ratios.
On the other hand, OG=l(K) may be achieved depending on the height OG of the center of gravity. Although it has been conventionally said that obtaining OG=l (K) is difficult for sea areas with relatively long wave lengths, such a case applies to ships with a general shape; and it is obtainable in box-type floating bodies having large breadth/draft ratios.
Realizing OG=l(K) through adjustment of the OG value may be achieved by, for example, making OG larger by installing a base on the box-type floating body to mount a heavy object on it. However, when OG is made larger, the value of GM becomes smaller, which may make the floating body unstable depending on its shape.
The present invention was made in view of the above and has its object to provide an anti-rolling structure for box-type floating bodies in which shapes of the box-type floating bodies are modified to adjust a value of moment lever l(K), thereby attaining OG=l(K) to reduce the wave exciting force.
In order to solve the above-mentioned problems, the present invention provides an anti-rolling structure for a box-type floating body comprising said floating body which is substantially rectangular when seen from above and at least a protrusion on at least either of transverse sides of the floating body, said protrusion extending longitudinally of the floating body at a level lower than a waterline.
Preferably, said longitudinal protrusion extends over substantially an entire length of the floating body.
Said longitudinal protrusion may extend partially of the floating body.
Preferably, in addition to the longitudinal protrusion at the level lower than the waterline, a plurality of vertical protrusions are arranged on the floating body and are spaced apart from each other longitudinally of the floating body, each of said vertical protrusions having a protruded dimension substantially equal to that of the longitudinal protrusion.
Preferably, the longitudinal protrusion is shaped such that height of center of gravity of the floating body substantially coincides with a moment lever acting on the floating body.
Preferably, the longitudinal protrusion is at a lower edge of the box-type floating body.
An operation of the invention will be described. A moment lever l(K) acting on a floating body, which depends on different factors such as an added mass synchronous coefficient of sway motion of the floating body and wave exciting force, can be obtained, as explained with FIG. 3, from the graph when the frequency is given with the breadth/draft ratio B/d as a parameter. With respect to an average frequency or period of waves in a sea area in which a floating body such as a hull of a work-ship or a hull for FPSO is installed, a value of the moment lever l(K) thus obtained does not usually coincide with height OG of the center of gravity except accidental coincidence. The value of OG may be adjusted to make it have the same value as or close to that of the moment lever, but such a way is not always practical. In the present invention, at least a longitudinal protrusion is provided on at least either of transverse sides of a box-type floating body at a level lower than a waterline to thereby adjust the moment lever l(K) to a value same as or close to that of OG. As a result, the wave exciting force is reduced for less roll motion of the box-type floating body.